演習問題

1. 次の関数の $f_{e}(x),f_{o}(x)$を求め,そのグラフを描け．
$$\begin{array}{l} (a) \ f(x) = \left\{\begin{array}{cl} x-1,& ... ...ay}\right . \ \ \ (b) f(x) = e^{x} \ x \in (0, \pi) \end{array}$$
2. 次の関数のフーリエ余弦,正弦級数を求めよ．
$$\begin{array}{ll} (a) \ f(x) = x^2 \ x \in [0,1] & (b) \ f(x)... ... [0,\pi] \\ (c) \ f(x) = \cos{x} \ x \in [0,\pi] & \end{array}$$
3. 次の関数の複素形フーリエ級数を求めよ．
$$\begin{array}{l} (a) \ f(x) = \vert x\vert \ x \in [-\pi,\pi] \ \ \ \ \ (b) \ f(x) = x^2 \ x \in [-\pi,\pi] \end{array}$$